Background

since the other parts of the program are specific only to that problem, I thought to post this generic part -calculating the area of a triangle in a cartesian coordinate system- in Code Project. This is for absolute beginners to help themselves with:

Comments and Discussions

I can't understand why you use !(area > 0) instead of area <= 0.
Nobody is so beginner that cannot understand it

Anyway, you used a formula that fits very well with distances, when working in the cartesian plan, that benefits much more from the nature of coordinates.
In order to evaluate the area of any polygon in the coordinates plan the easiest approach is compute the area of all the trapezoids built by the x axis, the y elevations of each vertex and the side of the polygon. And you can cycle, too.